Pith Number

pith:AOJUPRXY

pith:2015:AOJUPRXYACWVTRQ27IVBRTE2HJ

not attested not anchored not stored refs pending

Freeness versus maximal degree of the singular subscheme for surfaces in $P^3$

Alexandru Dimca

arxiv:1509.02106 v2 · 2015-09-07 · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AOJUPRXYACWVTRQ27IVBRTE2HJ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:36:33.553187Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

039347c6f800ad59c61afa2a18cc9a3a5d0ce306cbb500e5adcf921a6ba78de8

Aliases

arxiv: 1509.02106 · arxiv_version: 1509.02106v2 · doi: 10.48550/arxiv.1509.02106 · pith_short_12: AOJUPRXYACWV · pith_short_16: AOJUPRXYACWVTRQ2 · pith_short_8: AOJUPRXY

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/AOJUPRXYACWVTRQ27IVBRTE2HJ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 039347c6f800ad59c61afa2a18cc9a3a5d0ce306cbb500e5adcf921a6ba78de8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1aba8899c38fdd5446e9a7d21584824ef6cdc75492dc878bb5c6f9bc862f305",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-09-07T16:18:56Z",
    "title_canon_sha256": "e2c4ae7c52613976295f565b11189ba56b53ee42627df558fedf3851ac8d9dad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.02106",
    "kind": "arxiv",
    "version": 2
  }
}